Find the general form of the antiderivative for the function f (x) = sin3x-2 / cos ^ x / 2.

Let’s find the derivative of our given function: f (x) = sin (x) – cos (x) + x ^ 2.

Let’s use the basic rules and formulas for differentiation:

(x ^ n) ‘= n * x ^ (n-1).

(sin (x)) ‘= cos (x).

(cos (x) ‘= -sin (x).

(u ± v) ‘= u’ ± v ‘.

Therefore, the derivative of our given function will look like this:

f (x) ‘= (sin (x) – cos (x) + x ^ 2)’ = (sin (x)) ‘- (cos (x))’ + (x ^ 2) ‘= cos (x) – (-sin (x)) + 2 * x ^ 1 = cos (x) + sin (x) + 2x.

Answer: The derivative in this case will be equal to f (x) ‘= cos (x) + sin (x) + 2x.